So, I've just been promoted from Lieutenant to Lieutenant Commander I and appearently I suppose to get a new ship, well I selected a cruiser class starship, but I still have my old ship. What gives? Why would I be offered a new ship and still retain my old one? How do I get the new ship that I selected?

Go to the shipyard and find the NPC that lets you 'Select your ship'

and the choose your new ship and make it your primary ship (or something along the lines of that)

I did...I went to the Requistion Starship, and spoke with Lt. Laurel and selected the Cruiser starship and then I went to the State Room to be congratulated and nothing else occured. I went back to Requistion Starship and spoke to Lt. Laurel again and now the cost of the Cruiser is $25,550....I'm stuck.

no, after you get the ship, go to the shipyard where the holographic ship is in the middle of the room. There you will see an option "Select your Ship". Then follow what is said above

Once you have got the free ship. Goto the shipyard and there's an NPC on the right of the round holographic ship. Talk to him and select your ship and then select Make Primary in the bottom right hand side.

I found it!

Thank you, you two!